Apr 24, 2013

Source: Mailed to me by Sudeep Kamath (PhD Student, UC at Berkeley, EE IITB Alumnus 2008) - He found it at http://puzzletweeter.com/

Problem:
A group of students are sitting in a circle with the teacher in the center. They all have an even number of candies (not necessarily equal). When the teacher blows a whistle, each student passes half his candies to the student on his left. Then the students who have an odd number of candies obtain an extra candy from the teacher.

Show that after a finite number of whistles, all students have the same number of candies.

Source: Mailed to me by Sudeep Kamath (PhD Student, UC at Berkeley, EE IITB Alumnus 2008) - He found it at http://puzzletweeter.com/

Problem:

Consider an n x n chessboard, where each square is arbitrarily chosen to be either black or white. Your goal is to make all squares in the chessboard white. At each step, you are allowed to "switch" a square, but each switch will toggle not only the particular square being switched, but also the 4 squares that are adjacent to it: Two vertically up and down and two horizontally up and down the square being switched. Note : At corners only 4/3 squares are toggled, while at the center all 5 squares are toggled.

Show how you can make the entire chessboard white.

Update (May 20 2013):Solution: Posted by JDGM in comments! Very academic solution to a very interesting problem! :) Thanks

Apr 18, 2013

Source: Mailed to me by Sudeep Kamath (PhD Student, UC at Berkeley, EE IITB Alumnus 2008) - He found it at http://puzzletweeter.com/Problem:An integer point in a plane is a point whose coordinates are integers.

Suppose we arbitrarily choose 5 integer points in a plane.

Show that we can always find 2 among these 5 integer points such that the line segment joining the 2 points contains at least 1 more integer point.

Apr 6, 2013

Problem:
You are given a 100 sided die. After you roll once, you can choose to either get paid the dollar amount of that roll OR pay one dollar for one more roll. What is the expected value of the game?
(There is no limit on the number of rolls.)

Amazon.com Mathematics Bestsellers

Buy me Coffee / Beer via Paypal/BTC

Pages

Search This Blog

Follow by Email!

About Me

I am an early stage technology investor at Nexus Venture Partners. Prior to this, I was a 3x product entrepreneur. Prior to this, I worked as a private equity analyst at Blackstone and as a quant analyst at Morgan Stanley. I graduated from Department of Computer Science and Engineering of IIT Bombay. I enjoy Economics, Dramatics, Mathematics, Computer Science and Business.

Disclaimer

This is a personal blog. Any views or opinions represented in this blog are personal and belong solely to the blog owner and do not represent those of people, institutions or organizations that the owner may or may not be associated with in professional or personal capacity. Any views or opinions are not intended to malign any religion, ethnic group, club, organization, company, or individual.

All content provided on this blog is for informational purposes only. The owner of this blog makes no representations as to the accuracy or completeness of any information on this site or found by following any link on this site. The owner will not be liable for any errors or omissions in this information nor for the availability of this information. The owner will not be liable for any losses, injuries, or damages from the display or use of this information.